162 Annalen der Physik * Cc5'(p, p'y)Cc'' and Cc5'(p, n y)Mn'' 7. Folge * Band 20, Heft 3/4 * 1967 Reactions By M. A. ABUZEID,M. I. EL-ZAIKI,N. A. MANSOUR,A. I. POPOV~), H. R. SAADand V. E. STORIZHKO~) With 6 Figures Abstract Total yields and angular distributions of 380 keV gamma rays from the Cr53 ( p ,n y ) MnS3 reaction have been measured for proton energies below 2.5 MeV. The experimental results are in good agreement with predictions of the statistical compound-nucleus theory. The angular distributions of 560 keV gamma rays upon the proton inelastic scattering on C P at E, =. 2.3, 2.4 and 2.5 MeV are isotropic, which is commensurate with a 'I2- assignment t o the first excited state of C P . 1. Introduction The status of the compound-nucleus (CN) correlation theory for inelastic nucleon scattering has recently been reviewed both from the theoretical point of view and from the relevant experimental data [I]. It has been found that the theory is very successful in explaining numerous measurements of the correlation function for neutron and proton inelastic scattering from mediumheavy nuclei. At present, the available data for ( p , n y ) and ( n , p y ) reactions are' somewhat meagre, and the degree of validity of the CN correlation theory for such processes is not known. Recently, the inelastic scattering of protons on Cr5O and Cr54has been studied in this laboratory a t proton energies below 2.5MeV . The experimental results for angular distributions are in reasonably good agreement with the predictions of CN theory. This motivated us t o investigate the W3 ( p ,n y ) Mn'3 reaction. Measurements on the C r t 3 ( p , n )MnE3reaction in the energy range E , = 1.42 - 2.47 MeV were reported by LOVINGTON e t al. , who observed more than one hundred resonances in the neutron yield. Gamma radiation from this reaction has been studied by MCCLELLANDE e t al.  and VALTERet al. [5) with a single crystal NaI(T1) spectrometer. Using a thick natural Cr-target, the total yield of 380 keV y-rays for an E, = 1.6 .. . 3.2 MeV and also the angular distribution at E , = 2.6 MeV have been measured . I n a more recent investigation, KIM [61 studied fluctuations in the differential crosssection of the Cr53( p ,n ) Mn53reaction. I n this paper we report the results of the cross-section measurements of ( p , p ' y ) and ( p , n y ) reactions on Cr53 in the proton-energy region E , = 1.8 .. 2.5 MeV. 1) On leave from Physico-Technical Institute, Kharkov, USSR. 163 M. A. ABUZEIDand co-workers: Cr53(p,p'y)Cr53and C ~ - ~ ~ ( p , n y )Reactions Mn~~ 2. Experimental Arrangement Protons were accelerated by the 2.5 MeV electrostatic generator of the UAR Atomic Energy Establishment. After momentum analysis, the incident beam was focussed onto a target by quadrupole lenses. The target chamber was a cylindrical brass cup 3.0 cm in diameter with a wall thickness of 0.05 cm. Selfsupporting enriched chromium targets were used. Table 1 shows the isotopic composition and thickness of the targets. After passing through the target the beam was stopped in a 5011 gold foil in order t o reduce the background. The total charge delivered t o the target was measured with a current integrator. Table 1 T h i c k n e s s a n d enrichment of t h e Crb3 t a r g e t s Percentage of isotopic impurity present Target Nucleus (350 I (352 I Crs I Cr54 Target thickness mg cm-2 - Single gamma-ray spectra were measured using 2"x 2" NaI(T1) crystals and recorded with a transistorized RCL-512 channel pulse-height analyser. Fig. 1 displays a typical gamma-ray spectrum taken a t E , = 2.5MeV. It can be seen t h a t 200, 380 and 560keV gamma-rays are present. The origin of the 200 keV line has not yet been established, but it may be due t o a neutron irradiation of the NaI(T1) crystal. The 380 keV line corresponds t o the decay of the M d 3 first excited level in the W 3 ( p , n )M d 3 reaction. The ground state threshold energy of this reaction is equal t o 1380 keV . The 560 keV line resulting from the inelastic proton scattering corresponds t o the decay of the first excited level of W3. 380 053, P Ep=E50HeV 8=90" I 70 I 20 I 60 50 CHANNEL NUMBER 30 I J 60 0 Fig. 1. Pulse-height distribution of gamma-rays from the enriched Crm target taken at F, = 2.5MeV 11* I 30 -Bo a I 60 90 Fie. 2. Gcmma-ray angular distributions for the CP((p,p'y)Cra reaction. Solid lines are least squares fits to experimental distributions 164 Annalen der Physik * 7. Folge * Band 20, Heft 3/4 * 19Gi 3. Results of the Measurements The angular distributions of 560 keV gamma rays following the inelastic scattering Cr53(p,p‘y)Cr53 have been measured a t E , = 2.3, 2.4 and 2.5 MeV. Fig. 2 shows the results of these measurements. All these angular distributions are isotropic, which is commensurate with a assignment  t o the first excited state of Cr53.The uncertainties are statistical errors only. The angular distributions of 380 keV gamma rays from the Cr53(I), reaction have been measured for the proton energy range 1.9...2.5MeV in steps of 100 keV. Fig. 3 shows the results of these measurements. Statistical errors in the recorded counts were negligible and are not indicated in Fig. 3. All the angular distributions are similar t o those measured a t E , = 2.6 MeV by VALTER et al. [ 5 ] . The gamma ray yield, for proton energies 1.9 t o 2.5 MeV, has been measured a t an angle of 56” with respect to the proton beam direction Fig. 4 shows the total gamma ray yield from the Cr53(p,ny)Mn53 reaction obtained from these measurement,s. 1 I . I9 - 20 2.7 22 23 24 2 5 Ep (MeVl Fig. 3. Gamma-ray angular distributions for the CrSS( p , n y )Mn53reaction. Solid lines are the theoretical CN fit Fig. 4. Total yield of the 380 keV gamma rays from the Crm(p,ny)Mns reaction. The solid line is the theoretical CK fit 4. Data Analysis The angular CN correlation theory developed by HAUSER and FESHBACH , SATCHLER [lo], and SHELDON[I] for inelastic nucleon scattering may be generalized for the (p,ny) and (n,py) processes. Energy levels involved in the CrE3 + p reactions are shown in Fig. 5 . Following SHELDON [l]we can write t h e differential cross-section of the Cr53( p ,n y ) Mn53 reaction for a transition M. A. ABUZEIDand co-workers: W3( p , p ' y ) CrS8 and Crj3 ( ~ , n y ) MReactions n~~ 165 J,,(j$*)) J1( j $ + ) )J2(LL') Js (intermediate radiation is not observed) in the form: dU - 2' (-)JL*)-Jl-Jz a-8 [Cj1 (32)2/(j~)21 )3 6 (&! T A(ji*) i$*)J OJ1) x 1"2.(J3J2) W(J1J,J2J,; Aja*)) T P A(cos O ) , with the summation over all permitted values of A, J1 and jb+). Here R(J3J2) FE (1 +i l y . [F).(LLJ3J,) + 2dF1(LL'J3J2) (1) + 42F~(L'L'J3J,)I fin" Fig. 5. Energy level diagram showing the transitions that were studied in the present work The mixing ratio A 2 = ' "L'llJa)'- FAand 71 are functions tabulated by FERENZ !J311L11J2)a + and ROZENZWEIG [ll]and SATCHLER ; j = (2J 1)1/*.The symbol d(*) confines the summation t o terms where the pairs of j ( * ) va.lues are numerically equal. The z terms are: t = fi?)(-WT i 3 3 2 ) i3 Tl*)(E), (2) where T(*) are generalized transmission coefficients (1). The total cross section for the CN mechanism may be written: 1 a = - - n2R 2 c [(j1)/@o)l2 t. (3) Jl,jL*) For the proton energy range studied, 1.9 t o 2.5 MeV, the average excitation energy of the levels in the MnM compound nucleus is 9.7 MeV. The mean CN level spacing was calculated using the GILBERT-CAMERON  theory and was found t o be 0.25keV. I n our measurements chromium targets were about 300 keV thick at the energies used. Therefore, many levels of the compound nucleus were excited, and the statistical model could be applied. However, it should be noted that, a t low bombarding energies, the effective CN level density may differ considerebIy from the calculated one, and the statistical assumption may be violated. Additional assumptions were introduced in the analysis of the Cr53(p,ny)M d 3 reaction: 1) only protons with 1 = 2 and neutrons with 1 = 3 contribute essentially t o the reaction; 2) the direct process cross section is small compared t o the CN cross section; 3) the only competing processes are the Cr53(p,no)Mn53reaction and proton inelastic scattering, the cross section of which is small compared t o t h a t of the ( p , n) reaction. All these assumptions are well satisfied in the proton energy range studied. A general 166 Annalen der Physik * 7. Folge * Band 20, Heft 314 * 19G7 form of the differential cross section for the (p,ny) reaction on a non-zero spin nucleus is quite cumbersome and not given here. The neutron transmission coefficients T i * ) ( E )were obtained through interpolation from the tables pub. The optical model potential was of the form: lished by NEMIROVSKY V = (1 + i t ) , V,exp[-a((r-R')] v = VO(1 + i t ) , rrR', r 2 R'. (4) cm2, (5) The parameters used in the calculations were : V, = 50 MeV, E = 0.06, a R, 1.55fm, = 1.24. All3 fm. x = 2.8. = These parameters were obtained from an analysis  of the total cross sections and angular distributions in the energy region below 1 MeV. The proton transe t al. mission coefficients have been calculated using the method of FESHBACH 1151. I n Fig. 3 solid lines represent results of the theoretical calculations for the angular distributions of gamma rays from the Cr53( p ,n y ) Mn53 reaction. The experimental and theoretical curves have been normalized arbitrarily. The value  of the mixing parameter d = 1.2 for the gamma transition 380 keV c g.S. i n Mn53has been used. As can be seen, the predictions of the CN theory are in reasonable agreement with the experimental results. The calculations without the inclusion of spin-orbit interaction display a n equally satisfactory agreement; the only marked discrepancy occurs a t E , = 1.9 MeV. However, the results of these measurements for this energy are, t o some extent, uncertain, since a contribution from the Cr52(p,y)Mn53 reaction may be essential. The measurements with an enriched Cr52 target show a larger anisotropy in the angular distributions for this reaction. Because of a small anisotropy in the angular distributions, the accuracy involved in the determination of the mixing parameter is very low. For this reason, the angular distributions for E , = 2.2, 2.3, 2.4 and 2.5MeV were averaged. The averaged distribution anisotropy A = -0.072 f 0.014 was determined by a least-squares fit from the ratio A = (I A2)/(1- 0.5.4,) - 1, where A , is the coefficient in the expansion W ( 0 ) = 1 A,P,(cos 0). (The shaded area in Fig. 6.) The averaged distribution anisotropy is compared with + + 0 0.5 I A 2 345 0) -A 0.70 008 a06 Or04 0.02 O0 30" 600 t0n-q --c 900 Fig. 6. Experimental asymmetry parameter (shaded area) and theoretical predictions for different values of the mixing parameter A (solid line) M. A. ABUZEIDand co-workers: Cr5a(p,p’y)CrSSand Cr53(p,ny)Mn53 Reactions 167 theoretical predictions. The solid line represents the results of the CN fit for various values of the mixing parameter A . The value of A determined from the analysis is A = 1.3 & 0.7, which is in accord with a n earlier measurement . I n Fig. 4, the solid line represents the calculated total yield of gamma rays from the Cr53(p,.ny) Mn53 reaction. The experimental and theoretical curves have been normalized arbitrarily. Good agreement between theory and experiment is found. Conclusion The present investigation of the (3% ( p ,n y ) Mn53 reaction shows that the over-all agreement between the predictions of the CN theory and the measured angular distributions, as well as the total gamma-ray yield, is quite good even below 2.5 MeV. Further study of the ( p , n y ) reactions is desirable t o establish the CN model adequacy for such processes. The authors are indebted t o Professor M. EL-NADI foi encouragement during this investigation. Grateful thanks are extended t o Dr.A. A. KRESNIK for discussions. The author’s thanks are also due t o the accelerator staff for efficient work as well t o A. OUZOYKENE for his help in preparing the article for publication. Two of us (A. I. P . and V. E. S.) would like t o thank the authorities of the UAR Atomic Energy Establishment for their hospitality. References [l] SHELDON, E., Rev. Mod. Physics 35 (1963) 795.  ABIJZEID, M. A., M. I. EL-ZAIKI, N. A. MANSOUR,A. I. POPOV,H. R. SAADand V. E. STORIZHKO (to be published). J. A., J. J. G . MCCUEand W. M. PRESTON, Physic. Rev. 85 (1952) 585.  LOVINQTON, C. L., C. GOOD-MANand P. H. STELSON, Physic. Rev. 86 (1952)  MCCLELLANDE, 631 A.  VALTER,A. K., I. 1.ZALOUBOVSKY, A. P. KLUCIIAREV and V. A. LOUTSIK,Nuclear reactions at low and medium energies (Academy of Science USSR, Moscow, 1958,279).  KIM, H. I., Oak Ridge National Laboratory Report No ORNL 0-674 (1954), Phys. Letters 14 (1965) 51. 171 JOHNSON, C. H., C. C. TRAIL,and A. GALONSKY, Physic. Rev. 136 (1964) B 1719. 25, D.C., sheet  Nuclear Data Sheets, National Academy of Sciences, Washington 61-3-47. HANSER, W., and H. FESHBACH, Physic. R.ev. 87 (1952) 368. SATCHLER, G. R., Physic. Rev. 94 (1954) 1304; 104 (1956) 1198. FERENZ, M., and N. ROSENZWEIG, Argonne Report ANL-5324 (1955). SATCHLER, G. R., Proc. physic. SOC.(London) A 66 (1965) 1081. Can. J. Phys. 48 (1966) 1446. GILBERT,A., and A. G. W. CAMERON, P. E., Modern Nuclear Models (Atomizdat, Moskow, 1960). NEMIROVSKY, FESHBACH, H., M.M. SHAPIRO, and V. F. WEISSKOPF, NYO-3377, NDA Report 15B-5 (June 15, 1953). Ca.iro (Egypt), Atomic Energy Establishment. Bei der Redaktion eingegangen am 29. Dezember 196G.